There is a good way to interpret the progression so that the B♭13 isn't out of place/being borrowed from a different mode. Think of the first two measures as being in F Dorian and the last two measures as being a iiø-V7alt in F min. The advantage of this approach is that there is more cohesion/continuity between the Fmin and B♭13 chords.
Think of B♭min as Gø7
The B♭min chord is serving a subdominant function: it preps the V7 chord, C7alt. In this way, it is interchangeable with Gø7. In fact, if we replaced B♭m9 with B♭m6 (which wouldn't change the function of the B♭m chord), then now the B♭m6 chord would be voiced B♭-D♭-F-G, which is also the exact spelling of a Gø7 chord. In general, ii-V-i progressions and iv-V-i progressions are both commonly found in music, and are often interchangeable.
Think of Fm9 in terms of F Dorian
Just as we could treat the B♭m9 chord as B♭m6, the Fm chord can be interpreted through many different scales (F melodic minor, F Dorian minor, F Aeolian minor, etc.). If you want the first two measures to be continuous, then you would choose F Dorian minor for measure 1, since F Dorian contains the D♮ from the B♭13 chord. In effect, you'd be treating the Fmin9 chord as Fmin6 (or more technically Fmin6/9). This interpretation/approach would create good cohesion in the first two measures, since both chords would now contain a D♮. When improvising, for example, an Fmin6 pentatonic scale would sound great (F-G-A♭-C-D) and would be seamless when passing from one chord to the next.
So ultimately, the way to think about this progression is as a i-IV7-iiø7-V7alt, with the first two measures using F Dorian and the last two measures being a turnaround:
| Fm6/9 | B♭13 | Gø7 | C7alt |
Other interpretations are possible. For example, you could interpret the Fm9 chord as implying F Aeolian (i.e., F natural minor). Doing this would cause the B♭7 chord to stick out more, because it'll be the only chord in the four measures that contains a D♮. One downside of using F Aeolian is that the D♭ will be an avoid note over the Fm9 chord, whereas the D♮ wouldn't. If you use F Dorian, then now the D♭ from C7alt can resolve down a half step to C or up a half step to D♮.
So if you're trying to make the B♭7 chord be more cohesive with the other chords, I recommend the approach I've outlined above. (Of course, if you're comping/playing chords behind a soloist, you want to listen to what the soloist is playing and let that dictate your choices too. If the soloist is playing a D♭ over the Fm9 chord, then avoid a D♮.)